Efficient linear schemes for a penalized ternary Cahn–Hilliard system

Department of Mathematics, University of North Texas, Denton, TX, USA

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 6 March 2025
Accepted: 8 April 2026

Abstract

In this work we introduce novel numerical schemes for a penalized version of the ternary Cahn–Hilliard system for the purpose of creating accurate and efficient numerical schemes of interfacial dynamics with three components as well as some results extending these ideas to systems with four or more components. The first scheme is linear, decoupled, first order accurate, and unconditionally energy stable. Next, we present a second scheme which is a conditionally energy stable modification of the first scheme, but has greatly reduced computational cost. Finally, we present a third scheme which is linear and second order accurate but the unknowns are coupled. Moreover, we present several numerical simulations in two and three dimensions to give a comprehensive overview of each scheme and the cost-benefit analysis associated with designing a method for energy-stability, efficiency, and accuracy.